Atletico Madrid are powerless to stop United swooping due to the striker’s £89million buy-out clause.
And now, according to The Sun, a £280,000-a-week contract offer has been accepted by the 26-year-old.
Jose Mourinho appears set to land his No1 target and bolster his frontline at Old Trafford.
Griezmann has outlined concerns about moving to the Premier League, including the weather in England.
But following Atletico’s 3-0 Champions League semi-final first leg defeat to Real Madrid on Tuesday, the wheels are in motion for his move to United.
The mammoth deal for Griezmann will apparently be for five years, and including wages and bonuses, the figure is set to reach £170m.
The hitman is said to have been handed reassurances by United about other signings this summer and an increase on an original contract offer.
Manchester United must pay his buy-out clause in one lump sum, but they are currently preparing for the process.